标题： DPNO：神经算子的双路径架构 显示英文标题

标题： DPNO: A Dual Path Architecture For Neural Operator

摘要： 神经算子已成为求解偏微分方程（PDEs）和其他复杂科学计算任务的强大工具。 然而，单个算子块的性能通常受到限制，因此通常需要组合基本算子块以实现更好的性能。 传统组合方式是像前馈神经网络一样堆叠这些块，这在考虑参数效率权衡时可能并不经济。 在本文中，我们提出了一种新颖的双路径架构，显著增强了基本神经算子的能力。 基本算子块以并行的两条路径组织，类似于ResNet和DenseNet。 通过引入这种并行处理机制，与原始模型相比，我们的架构显示出更强大的特征提取和解决方案逼近能力。 我们通过在多种PDE问题上的广泛数值实验验证了我们方法的有效性，包括Burgers方程、Darcy流方程和2d Navier-Stokes方程。 实验结果表明，在某些标准测试用例上，我们的模型相比基本模型实现了超过30%的相对改进。 我们将这种结构应用于从不同范式中选择的两个标准神经算子（DeepONet和FNO），这表明所提出的架构具有出色的通用性，并为神经算子结构设计提供了一个有前景的方向。 显示英文摘要

摘要： Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring composition of basic operator blocks to achieve better per-formance. The traditional way of composition is staking those blocks like feedforward neural networks, which may not be very economic considering parameter-efficiency tradeoff. In this pa-per, we propose a novel dual path architecture that significantly enhances the capabilities of basic neural operators. The basic operator block is organized in parallel two paths which are similar with ResNet and DenseNet. By introducing this parallel processing mechanism, our architecture shows a more powerful feature extraction and solution approximation ability compared with the original model. We demonstrate the effectiveness of our approach through extensive numerical experi-ments on a variety of PDE problems, including the Burgers' equation, Darcy Flow Equation and the 2d Navier-Stokes equation. The experimental results indicate that on certain standard test cas-es, our model achieves a relative improvement of over 30% compared to the basic model. We also apply this structure on two standard neural operators (DeepONet and FNO) selected from different paradigms, which suggests that the proposed architecture has excellent versatility and offering a promising direction for neural operator structure design.